Problem: What do the following two equations represent? $-3x+3y = 5$ $-9x-9y = 5$
Answer: Putting the first equation in $y = mx + b$ form gives: $-3x+3y = 5$ $3y = 3x+5$ $y = 1x + \dfrac{5}{3}$ Putting the second equation in $y = mx + b$ form gives: $-9x-9y = 5$ $-9y = 9x+5$ $y = -1x - \dfrac{5}{9}$ The slopes are negative inverses of each other, so the lines are perpendicular.